Calculus of Variations and Geometric Measure Theory
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B. Bogosel - B. Velichkov

A multiphase shape optimization problem for eigenvalues: qualitative study and numerical results

created by velichkov on 03 Dec 2013
modified on 27 Sep 2015

[BibTeX]

SINUM

Inserted: 3 dec 2013
Last Updated: 27 sep 2015

Year: 2013

Abstract:

We consider the multiphase shape optimization problem

$\min\Big\{\sum_{i=1}^h\big(\lambda_1(\Omega_i)+c \vert
\Omega_i \vert
\big):\ \Omega_i\ \hbox{open},\ \Omega_i\subset D,\ \Omega_i\cap\Omega_j=\emptyset \Big\},$

where $c>0$ is a given constant and $D\subset\mathbb{R}^2$ is a bounded open set with Lipschitz boundary. We give some new results concerning the qualitative properties of the optimal sets and the regularity of the corresponding eigenfunctions. We also provide some numerical results for the optimal configuration.

Keywords: monotonicity formula, shape optimization, eigenvalues, multiphase, optimal partition


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